Timing and Synchronization of Low Data Rate Ultra-wideband Systems using Data-aided Auto-correlation Method

Transcription

1 Timing and Synchronization of Low Data Rate Ultra-wideband Systems using Data-aided Auto-correlation Method by Rongrong Zhang B. Eng., Shanghai Jiao Tong University, Shanghai, China, 2004 A Thesis Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Applied Science in the Department of Electrical and Computer Engineering c Rongrong Zhang, 2008 University of Victoria All rights reserved. This thesis may not be reproduced in whole or in part by photocopy or other means, without the permission of the author.

2 Timing and Synchronization of Low Data Rate Ultra-wideband Systems using Data-aided Auto-correlation Method ii by Rongrong Zhang B. Eng., Shanghai Jiao Tong University, Shanghai, China, 2004 Supervisory Committee Dr. Xiaodai Dong, Supervisor (Department of Electrical and Computer Engineering) Dr. Aaron Gulliver, Member (Department of Electrical and Computer Engineering) Dr. Jianping Pan, Outside Member (Department of Computer Science) Dr. Kui Wu, External Examiner (Department of Computer Science)

3 iii Supervisory Committee Dr. Xiaodai Dong, Supervisor (Department of Electrical and Computer Engineering) Dr. Aaron Gulliver, Member (Department of Electrical and Computer Engineering) Dr. Jianping Pan, Outside Member (Department of Computer Science) Dr. Kui Wu, External Examiner (Department of Computer Science) Abstract For low data rate ultra-wideband (UWB) communication systems employing noncoherent detection and autocorrelation detection schemes, timing of integration region significantly affects their error rate performance. Time-of-arrival (TOA) estimation of the first channel tap is also the foundation of the UWB based ranging applications. In this thesis, a data-aided, autocorrelation based timing and synchronization method is developed. First, estimation of the optimal integration region, i.e., the initial point and the length of the integration, using the new timing method is presented. It is shown that the proposed method enhances the error rate performance compared to non-optimal integration region-determining methods. After that, TOA estimation using the proposed timing method is studied for the dual pulse (DP) signal structure. The performance improvement of this approach over the conventional energy detection based method is demonstrated via simulation.

4 iv Table of Contents Supervisory Committee ii Abstract iii Table of Contents iv List of Tables vi List of Figures vii List of Acronyms x Acknowledgements xiii Dedication xiv 1 Introduction Brief Overview of Ultra-wideband Communication Strengths and Possible Applications of Low Data Rate UWB Thesis Outline UWB Communication System 11

5 v 2.1 UWB Impulse Radio UWB Channel Model UWB Modulation and Detection Schemes Integration Region Optimization for Non-Coherent Detection and Autocorrelation Detection UWB Systems Background BER Performance Analysis Optimization Using Training Sequence Simulation Results Summary Time of Arrival Estimation Using Dual Pulse Signals Background TOA Estimation Using Autocorrelation Analysis on P fa, P m and MAE of the Proposed TOA Method Simulation Results Summary Conclusions and Future Work Conclusions Future Work

6 List of Tables vi

7 vii List of Figures 1.1 FCC spectral mask for indoor commercial UWB systems [1] The RRC pulse used in this thesis is compliant with the standard The spectrums of the RRC pulse and second order Gaussian pulse The second order Gaussian pulse used for comparison CIR of two UWB channel model realizations [26]. The upper plot is a CM1 realization and the lower plot is a CM8 realization Illustration of (a) the transmitted signal and (b) R{r(t)r (t T p )} of the DP system. The labeled time intervals in (b) correspond to the flat regions (noise region (NR) of -1, NR of +1 ) and the monotonically decreasing region (signal region (SR) of +1 ) that the noiseless part of x(τ) in eq. (4.2) experiences Received TR signal (noiseless) r (i) (t) and r (i+1) (t), N f = Typical curve of x(τ) with detailed display of the threshold and estimated T

8 viii 3.3 The effect of a timing error on the BER performance of the noncoherent and TR schemes. The top two plots represent error in T 0 and T for CM1 channels; the bottom two plots represent error in T 0 and T for CM8 channels The distribution of the optimal integration region and the corresponding BER of 50 CM1 and CM8 channel realizations BER obtained with 5 different integration regions for PPM non-coherent detection in CM1 and CM8 channel realizations BER obtained with 5 different integration regions for transmitted reference in CM1 and CM8 channel realizations The effect of fixing γ in (3.15) for CM1 channels The effect of fixing γ in (3.15) for CM8 channels The effect of different training sequence length on the performance of PPM non-coherent detection in CM1 and CM8 channel realizations. Eq. (3.18) is used for averaging The effect of different training sequence length on the performance of transmitted reference in CM1 and CM8 channel realizations. Eq. (3.19) is used for averaging The BER performance of 5 different integration region determining methods. The top plot represents the N f = 2 case, the bottom plot represents the N f = 4 case The noisy x(τ) curve with an example threshold crossing of η = 0.9 and E b /N 0 = 16 db

9 ix 4.2 The probability of early false alarm and probability of missed-directpath errors of the proposed TOA estimation method in CM1 channels with fixed thresholds, N = 32, and T b = 1 ns The probability of early false alarm and probability of missed-directpath errors with normalized threshold η, N = 32 and T b = 1 ns The effect of different values of normalized threshold η on the mean absolute error, with N = 32 and T b = 1 ns. Solid lines represent the DP based estimation method, dashed lines represent the ED based estimation method with perfect coarse timing, and dashed-dotted lines represent the ED based method without coarse timing MAE versus normalized threshold for different SNR values in CM1 channels with N = 32 and T b = 1 ns The mean absolute error of using a 2nd order Gaussian pulse with different values of the normalized threshold, N = 32 and T b = 1 ns. The solid lines represent DP based estimation method, and the dashed line represent the ED based estimation method without coarse timing The mean absolute errors with different search stepsize T b in CM1 channels, and N = The effect of different training sequence length N on the DP based TOA estimation performance, with η = 0.9 and T b = 1 ns The mean absolute errors of the proposed TOA estimation method in CM4 channels with N = 32 and T b = 1 ns

10 x List of Acronyms ADC AWGN BER BPPM CDMA CIR CM DoD DP DS ED FCC GML GPS IEEE analog-to-digital converter additive white Gaussian noise bit error rate binary pulse position modulation code division multiple access channel impulse response channel model Department of Defense dual pulse direct sequence energy detection Federal Communications Committee generalized maximum likelihood global positioning system Institute of Electrical and Electronics Engineers

11 xi IEEE-SA IFI IPI IR ISI MAE MB-OFDM MED (N)LOS NR PAPR PAR PDP PN PPAM PSD RF RRC SNR SR TC IEEE Standards Association inter-frame-interference inter-pulse-interference impulse radio inter-symbol-interference mean absolute error multiband orthogonal frequency division multiplexing maximum energy detection (non)-line-of-sight noise region peak-to-average power ratio project authorization request power delay profile pseudorandom noise pulse position amplitude power spectral density radio frequency root raised cosine signal-to-noise ratio signal region threshold crossing

12 xii TG TH-PPM TOA TR UWB WPAN task group time-hopping pulse position modulation modulation time of arrival transmitted reference ultra-wideband wireless personal area network

13 xiii Acknowledgements First and foremost I would like to thank my supervisor, Dr. Xiaodai Dong, for her valuable guidance, continuous encouragement and insightful technical advice throughout my study. This thesis work could not have been completed without the support and help from Dr. Dong. I would also like to thank Dr. Aaron Gulliver and Dr. Jianping Pan for the valuable suggestions on revising my thesis. Thanks to many of my colleagues and friends at University of Victoria for being so nice and helpful, which makes my stay in this foreign country a great pleasure. Especially, I would like to thank Dr. Yue Wang, Dr. Wei Li, Li, Fengdan, Massoud, Shiva, Ruonan and Omar for their priceless help. Special thanks to Steve, Erik, Duncan, Vicky, Sarah, Moneca, Lynne and Mary- Anne for the many patient and constant help from them. Last but not least, I would like to thank my wife and parents for being so supportive all through these years. It is hard to put into words how much I appreciate their love and how grateful I feel to have them with me.

14 xiv Dedication To my dear wife, Amy Shen

15 Chapter 1 Introduction Ultra-wideband (UWB) technology is a promising candidate for low power, low complexity, short distance communications. Ever since the Federal Communications Committee (FCC) granted the unlicensed GHz spectrum for UWB systems [2], a large number of UWB techniques, algorithms and product prototypes have been developed each year. In August 2007, IEEE standard board approved UWB as an alternative physical layer technology for low-rate wireless personal area network (WPAN) applications (IEEE a [3]). It is reasonable to expect that the debut of UWB based personal communication products on the wireless market is not far away. In this chapter, a brief overview of ultra-wideband technology is presented from a historical perspective, with focus on the recently standardized low data-rate UWB techniques. Strengths and challenges of low data-rate UWB applications are introduced, which lay as the foundation and start point of the research that forms this thesis.

16 2 1.1 Brief Overview of Ultra-wideband Communication Ultra-wideband communication is not a new technology at all. When Guglielmo Marconi started his pioneer works of wireless telegraph transmission, the information was conveyed on a series of electrical sparks, which is nothing but carrierless, impulse based, ultra-wideband communication. During 1960s and 1970s, UWB has been developed for applications such as radar systems and ground penetrating geological survey systems [4]. Ross, Robbins and other researchers made some of the earliest contributions to the UWB communication systems [4]. However, the terminology Ultra-Wideband did not come into being until 1989 when the U.S. Department of Defense (DoD) decided to use this term for devices occupying a bandwidth no less than 1.5 GHz or a -20 db fractional bandwidth exceeding 25% [1]. In April 2002, FCC released its first report and order (R&O) about UWB communications, in which it granted the bandwidth below 960 MHz and from 3.1 GHz to 10.6 GHz for UWB use [2]. The FCC spectral mask for indoor UWB systems is shown in Fig. 1. Specifically, the FCC spectrum mask requires the power spectral density (PSD) of indoor UWB transmitted signal to be smaller than dbm/mhz, which is the Part 15 limit for spurious radio frequency (RF) emission, for the frequency bands below 960 MHz and between 3.1 GHz 10.6 GHz. This means the UWB signal is below the noise floor of other systems that share the spectrum with it. Moreover, the UWB signal shall be below -75 dbm/mhz between 0.96 GHz to 1.61 GHz, which gives way to near-noise-floor communications such as global positioning system (GPS). The first R&O also redefines UWB as a system with a -10 db bandwidth no less

17 3 Figure 1.1: FCC spectral mask for indoor commercial UWB systems [1]. than 500 MHz or a fractional bandwidth exceeding 20%. The fractional bandwidth is defined as B/f c, where B = f H f L is the -10 db bandwidth with f H being the upper frequency of the -10 db emission point and f L being the lower frequency of the -10 db emission point, and f c (f H + f L )/2. According to Shannon s theorem on channel capacity, the maximum information rate of a band-limited additive white Gaussian noise (AWGN) channel follows [5] C = W log(1 + P av WN 0 ) (1.1) where W is the signal bandwidth, P av is the average power of the transmitted signal, and N 0 is the noise variance. Eq. (1.1) shows that given a certain amount of transmit power and noise variance, a larger bandwidth yields a greater channel capacity. For

18 4 example, supposing the signal to noise ratio P av /WN 0 is as low as 0 db, if the whole 7.5 GHz regulated bandwidth is efficiently utilized, the data rate could be 7.5 Gbps. Therefore, even if the PSD of UWB signal is limited to a sub-noisefloor level, at least in theory the UWB systems are able to achieve much higher data-rate than the currently used narrowband and wideband systems. From another perspective, given the ultra-wide bandwidth, a much lower transmitted power is sufficient for communication at a comparable speed to existing wireless systems. High data-rate, low power, along with other features such as high time resolution, ability of penetrating objects, great security ability, etc., provide strong motivations for people to pursue advances in the UWB technology. Two task groups (TGs) were formed by IEEE to study the possibility of adopting UWB as an alternative physical layer option for wireless personal area network (WPAN) (range from 1 m to 10 m). TG a is aiming at providing a higher speed UWB physical layer enhancement amendment to IEEE for applications which involves imaging and multimedia transmission; TG a is targeting at communications and high precision ranging/localization systems (1 meter accuracy and better) with high aggregate throughput, ultra low power and low cost. Two technical proposals have been filed to TG3a. One is a single carrier UWB using direct sequence (DS) spread spectrum technology introduced by XtremeSpectrum [6], and the other is a multiband orthogonal frequency division multiplexing (MB-OFDM) based technology suppported by the Multiband OFDM Alliance (MBOA) [7]. DS-UWB transmits ultra-short pulses at baseband using the whole available spectrum, thus frees the requirements on (de)modulator. But otherwise it is similar to the conventional CDMA technology, and suffers from complicate design

19 5 of rake receivers to collect enough multipath diversity for reasonable system performance. On the other hand, MB-OFDM transmits signals using a 128-subcarrier OFDM scheme occupying a 500 MHz band. The signal band is frequency hopped in the available spectrum on a block-by-block basis. Although OFDM systems have simple receiver architecture, it also has drawbacks, such as OFDM s inherent high peak-to-average power ratio (PAPR) [8]. Since neither of the technologies has dominant advantage over the other, the standardization went into a deadlock. In January 2006, TG3a decided to withdraw the December 2002 project authorization request (PAR) that initiated the development of high data rate UWB standards and leave the decision to the market. If there is a surviving approach in a year or two and the technology has proven itself to be commercially viable, then IEEE will come back and revisit whether it makes sense to create an IEEE standard for it. Similar to high data rate UWB, a number of techniques have been developed as candidates for low data rate UWB applications. These include time-hopping pulse position modulation (TH-PPM) [9], pulse position amplitude modulation (PPAM) [10], transmitted reference (TR) [11], dual pulse (DP) [12], etc. But unlike TG3a, TG4a was able to reach an accordance on a draft standard, which was officially approved by IEEE-SA Standard Board on March 22nd, 2007 as an amendment to IEEE Std [3]. The standard specifies a clustered pulse train signal pattern, a regulation on the transimtted pulse shape and operating frequency bands, but leaves large freedom in signal structure and receiver design. According to the standard, each transmitted information symbol may contain either a single or multiple of clustered pulse trains. The number of pulses per clustered pulse train varies from 1

20 6 to 128. This clustered pulse train pattern is compatible with all of the aforementioned low data rate UWB signal schemes. This provides the opportunity and possibility for researchers to develop novel receiver algorithms for various applications. 1.2 Strengths and Possible Applications of Low Data Rate UWB Typically a low data rate UWB signal consists of a series of sub-nanosecond pulses. The bandwidth of the signal is roughly the reciprocal of the pulse duration, which ranges from 500 MHz up to a few GHz. Besides the benefit of low transmit power, as mentioned in the previous section, the UWB signal enjoys the following strengths as well. 1. High multipath diversity Because the UWB pulse has ultra-short duration, the possibility that pulses from two different multipaths overlap and cancel each other is much less than in narrowband systems. Intuitively, rich multipath diversity enhances the reliability of the wireless link since it increases the possibility that at least some of the multipath signal can go around obstacles. In other words, the multipath fading is less significant in a UWB system. A discrete equivalent UWB channel is usually comprised of hundreds of densely located multipath taps. A large amount of multipath diversity can be obtained if the signal energy on most of the multipath taps is collected by the receiver. 2. High timing resolution Timing resolution is inversely proportional to the bandwidth of the signal [13].

21 7 Because of the giga-hertz bandwidth of the UWB signal, the timing resolution is in the order of nano-seconds, which leads to a centimeter-level ranging capability. 3. High security The sub-noise floor transmitted power of the UWB signal, along with the great variety of signal pattern possibilities, makes UWB signal virtually impossible to be detected by a third party. UWB may be the most secure means of wireless transmission technology available. 4. Co-existence with narrowband and wideband systems Since the power spectral density of UWB signal is below the FCC Part 15 limit, it introduces only negligible interference into the existing narrowband and wideband communication systems. This allows UWB systems to be adopted in various indoor applications without worrying about affecting co-existing systems. Attributed by these merits, UWB is well suited to a lot of applications. First of all, UWB could be the communication backbone of the future digital home [14]. UWB wireless link can be used for sharing audio, video and data files between TV, computers, printers and consumer electronics. Connecting to a sensor network, it can also be used to wirelessly control the house heating and lighting systems to achieve best energy efficiency. Besides, UWB can be used in medical imaging systems, where small devices could be injected into human bodies to actually see the illness area and transmit the image back via a low power UWB connection. Moreover, with its accurate ranging capability, UWB can be used to enhance location based services [15]. UWB localization devices can be attached to infants at

22 8 home, inmates at prison or packages in a logistic warehouse for better surveillance; accurate localization systems can also help fire fighters and earthquake or mine accident rescuers to get better knowledge about the location of themselves. However, the ultra-wide bandwidth and low power also impose quite a few challenges on UWB system implementation. With current analog-to-digital converters (ADCs), it is impractical to sample the UWB signal at Nyquist rate which may be several GHz. Analog correlation and frame rate sampling are suggested in most of the proposed system designs, e.g., [16 19]. The great number of multipath taps brings difficulties on channel estimation and full-rank rake receiver implementation [1,20]. Alternatives such as selective rake receivers with partial channel estimation or transmitted reference autocorrelation receivers are used in the literature (see [21] and references therein). Due to the wide bandwidth distinct frequency components may experience different channel environments, causing distortion on the UWB pulse shape [22], which adds extra difficulty in coherent detection. Although UWB signals have fine timing resolution, achieving this resolution is not easy [15]. On one hand, the nanosecond pulse duration requires the UWB receiver to have nanosecond clock accuracy. Even the slightest timing jitter compromises the accuracy of the ranging result. On the other hand, ultrashort pulse duration and relatively long multipath delay spread extend the uncertainty region of timing and synchronization, which increases the possible delay positions to be searched.

23 9 1.3 Thesis Outline The research that forms this thesis mainly tackles the last challenge in the previous section. A data-aided timing and synchronization method is proposed for UWB systems. The proposed method bypasses the first three challenges mentioned in the last section. That is, the proposed method is based on non-coherent and autocorrelation receivers, thus requires neither channel estimation nor rake receiver. By using a training sequence, the proposed method is able to work at frame rate sampling. Furthermore, the proposed method is also applied on a dual pulse (DP) system to achieve a more accurate time-of-arrival (TOA) estimation which can be directly used for localization. Because the proposed timing and synchronization algorithm focuses on low data rate UWB systems, from the next chapter on the term UWB denotes low data rate UWB. High data rate UWB systems are generally not in discussion, unless otherwise specifically mentioned. The rest of the thesis is organized as follows. Chapter 2 formulates the UWB system in discussion. Particularly, the UWB systems with pulse position modulation, transmitted reference systems and dual pulse systems are discussed. Different receiver schemes, such as coherent receiver, non-coherent receiver with square-law detection and autocorrelation receiver are described. On top of that, a brief introduction to the UWB channel model is also included in this chapter. In Chapter 3, a method of timing and synchronization is presented. The method is able to estimate the optimal integration region, i.e., the initial point and the

24 10 length of the integration, for the non-coherent and autocorrelation receivers. Following a theoretical BER analysis, a data-aided estimation method using the idea of inter-symbol correlation is proposed. It is shown that using noise corrupted received signals, the proposed method is not only practically applicable, but also enhances the performance compared to non-optimal timing methods. In Chapter 4, the timing method is modified for TOA estimation using the DP signal structure. Inter-symbol signal autocorrelation and threshold crossing are used to detect the direct path in a line-of-sight (LOS) channel. The effects of different threshold values and training sequence lengths on the estimation accuracy of the proposed method are studied. The performance improvement of this approach over the conventional energy detection based method is also demonstrated via simulation. Finally, Chapter 5 concludes the thesis and suggests future research topics.

25 Chapter 2 UWB Communication System 2.1 UWB Impulse Radio One prevailing way to realize ultra-wideband communication is through impulse radio (IR), which is characterized by the usage of unmodulated, nanosecond-width pulses with a very low duty cycle. The ultra-narrow pulse duration makes it possible to spread the energy over a large bandwidth, which may range from near DC to a few gigahertz. To avoid inter-symbol-interference (ISI) and inter-frame-interference (IFI), adjacent pulses or pulse clusters are separated further than the longest channel delay spread, making the transmitter to work at only a small fraction of time, and remain silent at most time. This allows the IR transmitter to operate with low power consumption. The shape of the pulse may vary from system to system. In some cases even multiple types of pulses may co-exist in one system [23]. As per IEEE a standard [3], a pulse p(t) is compliant to the standard if its normalized cross-correlation with the reference pulse r(t) has a main lobe greater than 0.8 for at least a duration of T w, and no side lobes above 0.3, regardless of the actual shape of the pulse. The

26 12 { 1 } correlation is defined as R ErE p r(t)p (t + τ)dt where E r and E p are the energies of r(t) and p(t), respectively. The reference pulse is a root raised cosine (RRC) pulse defined as r(t) = [ 4β cos (1+β)πt π T p T p ] + sin[(1 β)πt/tp] 4βt/T p (4βt/T p ) 2 1 (2.1) where β = 0.6 is the roll-off factor and T p is the width of the reference pulse. The minimum main lobe width T w is 0.5 ns for pulses of 500 MHz bandwidth and 0.2 ns for pulses with larger bandwidth Root Raised Cosine pulse p C (t) UWB Reference pulse r(t) Correlation of p C (t) and r(t) time (ns) time (ns) time (ns) Figure 2.1: The RRC pulse used in this thesis is compliant with the standard. In this thesis, an RRC pulse p C (t) with 500 MHz bandwidth is used as transmitted

27 RRC pulse Gaussian pulse Power spectral density (dbm/hz) Frequency (Hz) x 10 9 Figure 2.2: The spectrums of the RRC pulse and second order Gaussian pulse. pulse in most of the simulations. It follows the same mathematical form as (2.1), but the roll-off factor of p C (t) is Fig. 2.1 shows the shape of p C (t), r(t) and their cross-correlation. It is shown that this pulse complies with the a standard as the main lobe of the normalized cross-correlation is greater than 0.8 for about 0.65 ns and no side lobe is greater than 0.3. Besides the RRC pulse, second order derivative of Gaussian pulse is used in the simulation in Chapter 4 to make a performance comparison between different pulse shapes. The second order Gaussian pulse is widely used in UWB literatures [1, 17,

28 Second order Gaussian pulse p G (t) UWB Reference pulse r(t) Correlation of p G (t) and r(t) time (ns) time (ns) time (ns) Figure 2.3: The second order Gaussian pulse used for comparison. 24,25]. Its mathematical representation is p G (t) = [1 4π(t/T p ) 2 ] e 2π(t/Tp)2 (2.2) where T p also denotes the pulse duration. With the same pulse duration, the second order Gaussian pulse has very similar -10 db bandwidth as the RRC pulse, as shown in Fig The pulse shape of p G (t) and its correlation with r(t) is shown in Fig Unfortunately, the second order Gaussian pulse does not comply with the IEEE standard because the side lobe of the cross-correlation is higher than 0.3, and the

29 15 main lobe is above 0.8 for only around 0.2 ns. In impulse radio UWB, data modulation is usually on the position or the polarization of the pulse, rather than on its magnitude or phase. This is because in a rich multipath environment it is more difficult to make a correct detection on the magnitude or phase of the received signal. Typically, one data symbol is comprised of several frames. Each frame may contain a single pulse, a pair of pulses, or a cluster of pulses. The information bit is modulated onto all these frames identically, which may be seen as a kind of repetition coding, which makes the i th transmitted symbol be s (i) (t) = E b N f N f 1 n=0 [ s (i) f t nt f T (i) c ] (n) (2.3) where E b is the transmitted energy per bit, N f is the number of frames per symbol, s f (t) denotes the signal within a frame where various modulation schemes can be applied and T (i) c (n) is a sequence of time delays for the frames in the i th symbol that is used to introduce time hopping to the system. Time hopping not only enables the system to accommodate multiple users, but also scrambles the transmitted signal so as to suppress the spectral spikes caused by the repetition of the signal. However, multiple access and scrambling are out of the scope of this thesis, thus are not included in the system model for timing and synchronization. As a result, T c (i) (n) is omitted in the following discussion. For systems with the proposed timing methods, time hopping can be adopted in the data transmission period once timing and synchronization are done.

30 UWB Channel Model As mentioned in Chapter 1, due to its ultra short pulse width, the UWB signal is able to resolve more multipath taps than conventional narrow band signals. This determines that the channel models used for narrow-band systems are no longer applicable for UWB studies. Based on various measurement results and modeling recommendations filed to the channel modeling subgroup of IEEE a, the task group proposed a generic UWB channel model in November 2004 [26]. It assumes the channel bins arrive in the form of clusters following the S-V model [27] and the channel fading is slow so that the channel stays constant during one block of data burst. According to the S-V model, the channel impulse response can be represented as h(t) = L K α k,l exp(jφ k,l )δ(t T l τ k,l ) (2.4) l=1 k=1 where T l denotes the delay of the l th cluster, τ k,l denotes the delay of the k th channel tap of the l th cluster relative to T l, α k,l and φ k,l denote the magnitude and phase of the k th channel tap in the l th cluster, respectively. The total number of clusters in the channel power delay profile (PDP) L is a random variable following Poisson distribution. That is p(l) = L L exp( L) L! (2.5) where L is the expectation of L. The cluster arrival time T l is defined as a Poisson process, i.e., the time difference of adjacent clusters follows the exponential distribu-

31 17 tion, which can be written as p(t l T l 1 ) = Λ exp[ Λ(T l T l 1 )], l > 0, (2.6) where Λ is the cluster arrival rate. On the other hand, the channel bin arrival time τ k,l is defined as the mixture of two Poisson processes, which is p(τ k,l τ (k l),l ) = βλ 1 exp[ λ 1 (τ k,l τ k 1,l )] + (1 β)λ 2 exp[ λ 2 (τ k,l τ k 1,l )], k > 0 (2.7) where β is called the mixture probability whose value varies over different channel environments, and λ 1 and λ 2 are the ray arrival rates. The tap gain α k,l follows Nakagami distribution. Its probability density function can be written as p αk,l (α) = Γ(m)( 2 m ) mα ( 2m 1 exp m ) α 2 Ω k,l Ω k,l (2.8) where m 1/2 is the Nakagami factor, Γ(m) is Gamma function and Ω is the mean square value of α. The Nakagami factor is modeled as a log-normal distributed random variable whose logarithm has mean m 0 and standard deviation ˆm 0. The mean power of the channel taps Ω k,l follows exponential distribution in each cluster. That is Ω k,l = Ω l exp( τ k,l /γ l ) γ l [(1 β)λ 1 + βλ 2 + 1] (2.9) where γ l is the intra-cluster decay time constant which is linearly dependant on the cluster arrival time, and Ω l denotes the total channel tap power within the l th cluster.

32 18 In [26], the above mentioned parameters, e.g. L, Λ, m0, etc., are specified for nine different scenarios, including indoor residential environments, indoor office environments, outdoor environments, indoor industrial environments and open outdoor environments, and the former four environments are divided into line-of-sight (LOS) and non-line-of-sight (NLOS) cases. Fig. 2.4 shows two examples of UWB channel realizations. The upper plot is the channel impulse response (CIR) of a realization of IEEE a channel model (CM) 1, which is an indoor residential LOS channel. It has relatively short root-mean-square delay and fewer channel taps. The lower plot is the CIR of a CM8 realization, which is an industrial NLOS channel. Its tap delay is much longer than the CM1 case and there is virtually no visible tap clustering. This is because in such an environment dense arrival multipath components are observed, which means that each resolvable channel tap contains significant energy. The channel model is thus virtually degraded to a conventional tapped delay line model with regular tap spacing. In the analysis of this thesis, the more general tapped delay line model is used for all environments instead of the more complicated model (2.4) just for representational clarity. It can be written as h(t) = L α l δ(t τ l ) (2.10) l=1 where L is the total number of resolvable multipath taps, α l and τ l are the complex magnitude and delay of the l th tap, respectively. However, in all simulations and numerical calculations, the channel model (2.4) as specified in [26] is used.

33 19 CIR of a CM1 Channel CIR of a CM8 Channel t (ns) t (ns) Figure 2.4: CIR of two UWB channel model realizations [26]. The upper plot is a CM1 realization and the lower plot is a CM8 realization. 2.3 UWB Modulation and Detection Schemes Three modulation schemes are studied in this thesis, including binary pulse position modulation (BPPM), transmitted reference (TR) and dual pulse (DP) schemes Binary Pulse Position Modulation The binary pulse position modulation is an orthogonal modulation. It equally divides one frame duration into two halves. Each frame contains a single pulse which locates in either the first half or the second half of the frame, depending on the data being

34 20 0 or 1. The BPPM signal of the i th symbol can be written as s (i) BPPM = E b N f N f 1 n=0 [ ] (1 d (i) )p(t nt f ) + d (i) p(t nt f T f /2) (2.11) where p(t) is the transmitted shaping pulse; d (i) {0, 1} is a binary input data. When the input data d is 0, the transmitted pulse locates at the first half of the frame; when d is 1, the pulse is at the second half of the frame. The frame duration T f is chosen to satisfy T f > 2(τ L τ 1 + T p ) so as to avoid IFI at the receiver, where T p is the duration of p(t) f(t) where f(t) is the receiver filter matched to p(t) and is operator of convolution. Denote g(t) p(t) h(t) f(t) as the impulse response of the equivalent channel, the received waveform of the i th symbol after passing through filter f(t) is given by r (i) BPPM (t) = E b N f N f 1 n=0 [ ] (1 d (i) )g(t nt f ) + d (i) g(t nt f T f /2) + n(t) (2.12) where the additive band limited complex Gaussian noise n(t) has a variance of N 0. Assuming an ideal low-pass filter (LPF) is used for f(t), the autocorrelation function of n(t) is R n (τ) = 2BN 0 sinc(2bτ), where B is the bandwidth of n(t), or equivalently the bandwidth of f(t). An LPF matched to p(t) can also be used in the receiver, bringing only slight modification on R n (τ). Due to the orthogonal nature of BPPM signaling, both coherent and non-coherent detection methods can be applied to demodulate the received signal in (2.12). For coherent detection, knowledge of the entire channel impulse response is required. In other words, a noiseless template of g(t) should be stored in the receiver.

35 Since the non-zero support of g(t) is [τ 1, τ L + T p ], the coherent detector performs cross-correlation in the following two time regions 21 N f 1 { τl y (i) +T p 1 = R n=0 n=0 τ 1 N f 1 { Tf y (i) /2+τ L +T p 2 = R T f /2+τ 1 r (i) BPPM (t + nt f) g (t)dt } r (i) BPPM (t + nt f) g (t)dt } (2.13) (2.14) where the operator denotes complex conjugate and R{x} takes the real part of x. The decision is then made by picking the greater one between y 1 and y 2, which can be written as y (i) y(i) 2. For non-coherent detection, the detector simply calculates the received signal energy in the two possible time slots in one frame, i.e., y (i) 1 = y (i) 2 = N f 1 n=0 N f 1 n=0 T0 +T T 0 Tf /2+T 0 +T T f /2+T 0 r (i) BPPM (t + nt f) 2 dt (2.15) r (i) BPPM (t + nt f) 2 dt (2.16) where T 0 and T are the start point and the length of the integration region, respectively. As in the non-coherent detection the channel state information is assumed to be unknown, the integration start point and length need to be estimated by the receiver. Because the choices of T 0 and T determine the integrated signal energy and noise energy, which are the decisive factors of the bit error rate performance of the system, both parameters need to be optimized according to the current channel condition. This is the target of the algorithm described in Chapter 3. Following the

36 integrations in (2.15)-(2.16), the decision is then made in the same manner as the coherent detection, as y (i) y(i) 2. In practice, the channel information is neither known by the transmitter nor by the receiver beforehand, and channel estimation from the noise corrupted received signal is shown to be overwhelmingly costly. Therefore, although non-coherent detection has poorer performance than the coherent detection, it remains a good compromise between complexity and performance Transmitted Reference Originally, the transmitted reference system was proposed in the 1960s for communications in the situation where the channel is unknown and difficult to estimate [28,29]. Since proposed by Hoctor and Tomlinson [11] as an alternative modulation scheme for UWB, transmitted reference scheme has drawn much attention among UWB researchers (see [17, 25, 30, 31], etc.). The advantage of the TR system is that the detector is simply an autocorrelator. No channel estimation is needed, as is the BPPM non-coherent detection. The main drawback of the TR system is its requirement on a wideband analog delay line for the receiver to realize the long time delay. This is not easy to implement. In a TR system, each frame contains two pulses. The first one that sits at the beginning of the frame is the reference pulse, and the second one which is delayed from the first pulse by T d is the data pulse. When the transmitting data is bit 0, the data pulse is a replica of the reference pulse; when a bit 1 is transmitted, the data pulse is the latter s antipode. The i th symbol of a TR signal can thus be represented 22

37 as s (i) TR = E b 2N f N f 1 n=0 23 [ ] p(t nt f ) + (1 2d (i) )p(t nt f T d ). (2.17) The frame duration T f in the TR system should also be at least 2(τ L τ 1 + T p ) so as to avoid IFI. Moreover, the time delay T d and the time difference between the data pulse and the reference pulse of the next frame should both be at least (τ L τ 1 +T p ) so as to avoid the inter-pulse-interference (IPI). Therefore, one convenient way to configure the TR signal structure is making T f exactly twice as T d. This is the case adopted in the discussion in Chapter 3, and thus T d will be replaced by T f /2 within the rest of this subsection and the next chapter. Similar to the BPPM case, the received TR signal after passing the receiver filter f(t) can be written as r (i) TR (t) = E b 2N f N f 1 n=0 [ ] g(t nt f ) + (1 2d (i) )g(t nt f T f /2) + n(t). (2.18) Autocorrelation detector is used to detect TR signals. It correlates the reference pulse with the data pulse, which is { Nf 1 y (i) TR = R n=0 T0 +T T 0 r (i) TR (t + nt f)r (i) TR (t + nt f + T f /2)dt }, (2.19) and then the decision is made as y (i) 1 TR 0. In (2.19), T 0 and T represent the integra- 0 tion start point and integration length, respectively. Similar to BPPM modulation with non-coherent detection, both parameters are not known a priori and thus need to be estimated and optimized at the receiver.

38 Dual Pulse Scheme Realizing the difficulty of implementing the T f /2 long wideband analog delay line in the TR system, Dong, et. al. proposed a dual pulse (DP) system that uses only pulse duration delay [12]. Similar to the TR signal, a dual pulse signal contains a reference pulse immediately followed by a data pulse in each symbol, as shown in Fig The transmitted DP signal of the i th symbol can be represented as s (i) DP (t) = E b 2N f N f 1 n=0 [ ] p(t nt f ) + (1 2d (i) )p(t nt f T p ). (2.20) Comparing (2.20) with (2.17), the delay between the reference pulse and the data pulse T d in conventional TR systems is longer than the channel maximum excess delay, but in the DP scheme T d equals to the pulse duration T p. Though certain amount of IPI is present in the DP system, it is shown that the system performance is just slightly degraded [12]. It is also found that the DP signal is an appropriate choice to realize the TOA estimation method proposed in Chapter 4. The received signal at the output of the receiver filter is given by r (i) (t) = E b 2N f N f 1 n=0 [ ] g(t nt f ) + (1 2d (i) )g(t nt f T p ) + n(t). (2.21) Autocorrelation is also used for data detection of the DP signal. The decision variable of the i th symbol is the following correlation { Nf 1 y (i) DP = R n=0 T0 +T T 0 r (i) DP (t + nt f)r (i) DP (t + nt f + T p )dt }. (2.22)

39 25 Figure 2.5: Illustration of (a) the transmitted signal and (b) R{r(t)r (t T p )} of the DP system. The labeled time intervals in (b) correspond to the flat regions (noise region (NR) of -1, NR of +1 ) and the monotonically decreasing region (signal region (SR) of +1 ) that the noiseless part of x(τ) in eq. (4.2) experiences. To further spread out the energy in the DP scheme into multiple DPs for lower peak-to-average power ratio, we can modify the transmitted signal to be a cluster of dual pulses spread by a pseudo random sequence, as given by s (i) (t) = Eb 2N c N f 1 n=0 N c 1 j=0 ] c j [p(t nt f 2jT p )+(1 2d (i) )p(t nt f 2jT p T p ) (2.23) where c j is the pseudo random code sequence with length N c. At the receiver, the received signal is matched to the following pseudo random pulse sequence c(t) = N c 1 j=0 c j p(t 2jT p ) (2.24) and the resultant signal is close to the single DP case for use in the autocorrelation based TOA estimation. In the subsequent discussion we will not distinguish the multi-dp scheme and the single DP scheme, while in the simulation single DP signal

40 is used. 26

41 Chapter 3 Integration Region Optimization for Non-Coherent Detection and Autocorrelation Detection UWB Systems 3.1 Background As mentioned in the previous chapters, coherent detection of UWB signals requires formidably complex channel estimation. Hence suboptimal receivers that do not require channel estimation were proposed for low complexity and low data rate applications, using either non-coherent detection of pulse position modulation signals (e.g., [32, 33]) or autocorrelation detection of transmitted reference signals (e.g., [11, 17]). These two schemes simply perform integration-and-dump operation at the receiver, which requires no channel estimation and only frame or symbol rate sampling. They yield reasonable performance with a sufficiently low complexity. For these schemes, the position and length of the integration region greatly affect their performance, because the start and end points of the integration determine how much signal energy

42 28 and noise energy will be captured, which in turn determines the bit error rate (BER). This issue was studied in some literature, e.g., [30,31,34]. In [30] and [31], the integration region was divided into a large number of smaller intervals, and a weighted summation was performed on the integration results so that the signal-to-noise ratio (SNR) at the detector is maximized. Both [30] and [31] focused on the methods of finding the optimal combining weights, while assuming the synchronization was done beforehand and the integration intervals were fixed. It is a different approach from the one in this paper, which does a synchronization first and then determines the position of the integration interval. In [34], synchronization for noncoherent schemes was performed iteratively until the integration interval is approximately the same as the signal region (SR), i.e., the time interval during which the transmitted pulses and their multipath components are received. This led to some performance improvement since the noise only region is excluded in the integration. However, covering the entire signal region is not necessarily an optimal solution. In this paper, determining the optimal integration region includes the estimation of two parameters: the start point of the integration and the length of the integration. The start point estimation is a similar problem to the fine synchronization that estimates the time of arrival (TOA) of the first significant tap. Previous literature, e.g. [35,36], proposed methods such as energy detection or maximum likelihood detection on the TOA estimation problem. Performance sensitivity to the timing inaccuracy of a non-coherent UWB system was derived in [24]. Theoretical discussion on the relationship between BER performance and the integration length of PPM non-coherent receivers and TR receivers can be found in [32] and [37], respectively. Except for the SNR maximization criterion derived, no practical method was given

43 29 on how to carry out the optimal integration length estimation in both papers. In this chapter, we develop an optimum integration region estimation method that is able to perform timing acquisition from the noise corrupted received signal. The method we propose is based on the idea of maximizing the captured receiving SNR at the integrator. In particular, we propose a data-aided approach that first performs a frame-level coarse timing, followed by accurate timing acquisition that determines the start point of the detection integration and then estimates the optimal integration length. The idea of data-aided timing using inter-symbol correlation can be traced back to previous research on the synchronization for UWB signals in [38] and [39]. These two papers studied frame-level synchronization, which is similar to the coarse timing step in our method. Since both [38] and [39] focused on bipolar modulation with coherent detection, they did not deal with the integration length problem. In this chapter, we further apply the idea of inter-symbol correlation with training sequence to non-coherent and autocorrelation schemes to perform fine timing and determine the optimal integration interval. Due to the transmitted reference signal structure, we are able to devise a relatively simple training sequence. The rest of this chapter is organized as follows. A theoretical BER performance analysis of the optimal integration region is given in Section 3.2. Section 3.3 proposes a practical estimation approach using training sequences. Section 3.4 presents some simulation results using the developed method and Section 3.5 gives concluding remarks.

44 BER Performance Analysis In this section, the performance analysis will first focus on BPPM modulation, and the results can be easily extended to the transmitted reference scheme thereafter. BPPM and TR signals follow the signal models in Chapter 2. Particularly, (2.15) and (2.16) are used to detect the BPPM signal. In the absence of IFI and IPI, demodulation and detection can be carried out symbol by symbol. Thus in the subsequent discussion in this section the index i is omitted for notation brevity. Intuitively, since more noise will be counted into the decision statistics with a longer integration length, the integration region should be chosen within the non-zero support of g(t), i.e., T 0 τ 1 and T 0 + T τ L + T p. Suppose in the i th symbol interval d = 0 is transmitted, the detector outputs are then given by T0 +T N y 1 = E b g(t) 2 E b f T0 +T dt + g(t)n (t + nt f )dt T 0 N f n=1 T 0 N E b f T0 +T N f T0 +T + g (t)n(t + nt f )dt + n(t + nt f ) 2 dt N f T 0 n=1 n=1 T 0 (3.1) E cap (T 0, T) + ζ 1 + ζ 2 + ζ 3 N f y 2 = n=1 where E cap (T o, T) = E b T0 +T T 0 Tf /2+T 0 +T T f /2+T 0 n(t + nt f ) 2 dt ζ 4 (3.2) g(t) 2 dt is the signal energy captured in the integration, ζ 1 and ζ 2 are the signal-noise cross terms, and ζ 3 and ζ 4 are the noise-noise cross terms. As shown in Appendix A, when T T p, they can be approximated as independent Gaussian random variables of which the distributions are respectively

45 31 ζ 1, ζ 2 N ( 0, N 0 E cap (T 0, T) ) and ζ 3, ζ 4 N ( 2N f N 0 BT, 2N f N 2 0 BT). Similar to the expression given in [32], the bit error rate of BPPM non-coherent detection is given by P e,ppm = P(y 1 < y 2 ) = P ( E cap (T 0, T) + ζ 1 + ζ 2 + ζ 3 ζ 4 < 0 ) ( Ecap 2 = Q (T ) 0, T) 4N f N0BT 2 + 2N 0 E cap (T 0, T) (3.3) where Q(x) 1 2π x e t 2 2 dt. Eq. (3.3) shows that the BER of BPPM signal largely depends on the choice of T 0 and T. Therefore the optimization of T 0 and T is equivalent to the maximization ( ˆT 0, ˆT) = arg max T 0,T E 2 cap (T 0, T) 4N f N 2 0 BT + 2N 0E cap (T 0, T). (3.4) Noticing that most of the energy in h(t) is in the front part while the latter part contains relatively small scattering and low-energy pulses traveling from far. By including the latter part of the signal region into the integration interval the additional collected signal energy may not compensate the additional noise energy. Therefore, the optimal integration length T is usually smaller than the length of signal region. Although the two-dimensional maximization in (3.4) can be solved by trying all the possible values within T 0 [τ 1, τ L +T p ] and T [0, τ L +T p T 0 ] for both variables, this approach has a computation complexity of O ( ( τ L+T p τ 1 ) 2), which grows rapidly t as τ L +T p τ 1 gets larger or the trying step size t gets smaller. In order to alleviate the computation task, we hope to fix one degree of freedom first and then perform the maximization over the other variable. It is found through simulation that deeming